Given a library of \(N\) \(^1\)H lung MRI with lung masks:
\(^1\)H\(_1\) + Mask\(_1\)
\(^1\)H\(_2\) + Mask\(_2\)
\(\vdots\)
\(^1\)H\(_N\) + Mask\(_N\)
First, we register the lung MRI library to the lung MRI to be segmented, \(^1\)H\(_u\),
Register(\(^1\)H\(_u\), \(^1\)H\(_1\)) \(\rightarrow\) \(T_1\)
Register(\(^1\)H\(_u\), \(^1\)H\(_2\)) \(\rightarrow\) \(T_2\)
\(\vdots\)
Register(\(^1\)H\(_u\), \(^1\)H\(_N\)) \(\rightarrow\) \(T_N\)
Each calculated transformation, \(T\), registers the corresponding database image to the unsegmented \(^1\)H MRI.
The MALF algorithm takes the following input:
\(^1\)H\(_u\)
the transformed lung MRI, i.e.,
\(T_1\)(\(^1\)H\(_1\)),
\(T_2\)(\(^1\)H\(_2\)), \(\ldots\),
\(T_N\)(\(^1\)H\(_N\))
the transformed lung MRI masks, i.e.,
\(T_1\)(Mask\(_1\)),
\(T_2\)(Mask\(_2\)), \(\ldots\),
\(T_N\)(Mask\(_N\))
Mask\(_u\) \(\leftarrow\) MALF(unsegmented \(^1\)H, transformed lungs, transformed masks)